## Periodic solutions of higher-dimensional discrete systems.(English)Zbl 1073.39010

The authors consider the second-order discrete system $\Delta^2X_{n-1}+ f(n, X_n)= 0,\quad n\in\mathbb{Z},\tag{1}$ where $$f\in C(\mathbb{R}\times \mathbb{R}^m, \mathbb{R}^m)$$, $$f(t+ M,\mathbb{Z})= f(t,\mathbb{Z})$$ for any $$(t,\mathbb{Z})\in \mathbb{R}\times \mathbb{R}^m$$ and $$M$$ is a positive integer. The existence of $$M$$ periodic solutions of (1) is proved.

### MSC:

 39A11 Stability of difference equations (MSC2000) 39A12 Discrete version of topics in analysis 34C25 Periodic solutions to ordinary differential equations

### Keywords:

second-order discrete system; periodic solution
Full Text: